Second-Order Systems Science: A Necessity-Driven Methodology for Coherence Under Acceleration

Modern socio-technical systems operate under unbounded composition of interventions, recursive self-modification, and accelerating novelty. First-order systems science—despite its local successes—fails structurally under these conditions due to incoherence: the degradation of navigability in functional state spaces under iteration and transfer. We show that coherence preservation imposes formal admissibility requirements (closure, contraction, alignment, coverage) that cannot be enforced without a second-order layer governing model updates themselves. This paper contributes a minimal coherence infrastructure for Second-Order Systems Science: a coherence compiler operating over a Typed Claim Language (TCL), a persistent ledger recording adjudication outcomes, and a strong-typing framework for research claims. The system detects—but does not resolve—incoherence by emitting explicit proof obligations when coherence cannot be established. We introduce Functional State Spaces (FSS) with typed operators, formalize the necessity conditions forcing ledgerization, and demonstrate feasibility through a collision experiment showing that prominent systems theories (Beer’s VSM, Luhmann’s SST), though individually coherent, are structurally incompatible under composition. The contribution is second-order epistemic infrastructure, not first-order theory: we provide machinery for detecting when theories can be compared, composed, or proven coherent—not which theories are correct. The accompanying compiler-grade specification enforces these constraints deterministically. We measured claim-extraction recoverability via five independent extractions: VSM core claims showed strong consensus, while SST and inference-sensitive claims exhibited lower agreement.